Goldstein was born to a Jewish family in Los Angeles, California and was raised in Beverly Hills. Her first film role was in James Cameron's Aliens (1987), playing the Hispanic character PFC Jenette Vasquez. She initially thought the role was about immigration due to the title and showed up for her audition to play a tough-as-nails space marine in a short skirt and high heels.

She also appeared as the vampire, Diamondback, in Near Dark (1987), Officer Meagan Shapiro in Lethal Weapon 2 (1989), Janelle Voight in Terminator 2: Judgment Day (1991), the Enterprise-B science officer in Star Trek Generations (1994), and an Irish immigrant mother in James Cameron's blockbuster, Titanic (1997).

Goldstein is the proprietress of the store Jenette Bras, a large-size bra specialist known for its slogan "The alphabet starts at D".